"""simple docstring"""






from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean

def 			lowerCAmelCase_   (_SCREAMING_SNAKE_CASE						:int	)					->			List[Any]:




						def is_in_circle(_SCREAMING_SNAKE_CASE						:float		,      _SCREAMING_SNAKE_CASE						:float	) -> bool:
												a_				:      Dict  		=       sqrt((x**2) + (y**2)	)
												# Our circle has a radius of 1, so a distance
												# greater than 1 would land outside the circle.
												return distance_from_centre <= 1

						# The proportion of guesses that landed in the circle
						a_				:      Union[str, Any]  		=       mean(
						    int(is_in_circle(uniform(-1.0		,      1.0	)		,      uniform(-1.0		,      1.0	)	)	)
						    for _ in range(lowercase_	)	)
						# The ratio of the area for circle to square is pi/4.
						a_				:      List[Any]  		=       proportion * 4
						print(F'''The estimated value of pi is {pi_estimate}'''	)
						print(F'''The numpy value of pi is {pi}'''	)
						print(F'''The total error is {abs(pi - pi_estimate	)}'''	)

def 			lowerCAmelCase_   (_SCREAMING_SNAKE_CASE						:int		,      _SCREAMING_SNAKE_CASE						:Callable[[float], float]		,      _SCREAMING_SNAKE_CASE						:float = 0.0		,      _SCREAMING_SNAKE_CASE						:float = 1.0		,      )					->			List[Any]:
						return mean(
						    function_to_integrate(uniform(lowercase_		,      lowercase_	)	) for _ in range(lowercase_	)	) * (max_value - min_value)

def 			lowerCAmelCase_   (_SCREAMING_SNAKE_CASE						:int		,      _SCREAMING_SNAKE_CASE						:float = 0.0		,      _SCREAMING_SNAKE_CASE						:float = 1.0	)					->			List[Any]:




						def identity_function(_SCREAMING_SNAKE_CASE						:float	) -> float:
												return x

						a_				:      Dict  		=       area_under_curve_estimator(
						    lowercase_		,      lowercase_		,      lowercase_		,      lowercase_	)
						a_				:      Any  		=       (max_value * max_value - min_value * min_value) / 2

						print("******************"	)
						print(F'''Estimating area under y=x where x varies from {min_value} to {max_value}'''	)
						print(F'''Estimated value is {estimated_value}'''	)
						print(F'''Expected value is {expected_value}'''	)
						print(F'''Total error is {abs(estimated_value - expected_value	)}'''	)
						print("******************"	)

def 			lowerCAmelCase_   (_SCREAMING_SNAKE_CASE						:int	)					->			Tuple:




						def function_to_integrate(_SCREAMING_SNAKE_CASE						:float	) -> float:
												return sqrt(4.0 - x * x	)

						a_				:      Dict  		=       area_under_curve_estimator(
						    lowercase_		,      lowercase_		,      0.0		,      2.0	)

						print("******************"	)
						print("Estimating pi using area_under_curve_estimator"	)
						print(F'''Estimated value is {estimated_value}'''	)
						print(F'''Expected value is {pi}'''	)
						print(F'''Total error is {abs(estimated_value - pi	)}'''	)
						print("******************"	)


if __name__ == "__main__":
				import doctest

				doctest.testmod()












'''simple docstring'''







# tests directory-specific settings - this file is run automatically
# by pytest before any tests are run

import sys
import warnings
from os.path import abspath, dirname, join


# allow having multiple repository checkouts and not needing to remember to rerun
# 'pip install -e .[dev]' when switching between checkouts and running tests.
__lowerCAmelCase        =							abspath(join(dirname(dirname(dirname(__file__))), "src"))
sys.path.insert(1, git_repo_path)


# silence FutureWarning warnings in tests since often we can't act on them until
# they become normal warnings - i.e. the tests still need to test the current functionality
warnings.simplefilter(action="ignore", category=FutureWarning)


def       __UpperCamelCase					(      lowercase_       :  Dict   ):
       """simple docstring"""




       from transformers.testing_utils import pytest_addoption_shared

       pytest_addoption_shared(lowercase_   )


def       __UpperCamelCase					(      lowercase_       :  List[Any]   ):
       """simple docstring"""




       from transformers.testing_utils import pytest_terminal_summary_main

       a_						     =			terminalreporter.config.getoption('--make-reports'   )
       if make_reports:
              pytest_terminal_summary_main(lowercase_   ,       id=lowercase_   )




